IN THE XY-COORDINATE SYSTEM, IF (A+B) ....

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factor26: Senior | Next Rank: 100 Posts; Posts: 99; Joined: Sun Mar 13, 2011 12:42 pm

by factor26 » Wed Sep 28, 2011 5:01 pm

In the xy-coordinate system, if (a, b) and (a + 3, b + k) are two points on the line defined by the equation x = 3y - 7, then k =
(A) 9
(B) 3
(C) 7/3
(D) 1
(E) 1/3

OA IS D ... can someone please give me a step by step on how to solve this and insight on topic being tested?

Thanks!

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user123321: Master | Next Rank: 500 Posts; Posts: 385; Joined: Fri Sep 23, 2011 9:02 pmFollowed by: 6 members; Thanked: 62 times

by user123321 » Wed Sep 28, 2011 5:27 pm

slope formed by these two points should be same as slope for the equation given.

slope of those points = (y2-y1)/(x2-x1) = k/3

slope of line is -a/b = -1/-3 = 1/3

equating both slopes => k/3 = 1/3 => k = 1

user123321

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Sep 28, 2011 5:48 pm

factor26 wrote:In the xy-coordinate system, if (a, b) and (a + 3, b + k) are two points on the line defined by the equation x = 3y - 7, then k =
(A) 9
(B) 3
(C) 7/3
(D) 1
(E) 1/3

OA IS D ... can someone please give me a step by step on how to solve this and insight on topic being tested?

Thanks!

Slope of a line passing through 2 points (x1, y1) and (x2, y2) = (y2 - y1)/(x2 - x1)
So, slope of the line passing through (a, b) and (a + 3, b + k) = {(b + k) - b}/{(a + 3) - a} = k/3
Now, slope of the given line x = 3y - 7 (or y = x/3 + 7/3) is 1/3.
Both the slope are equal, so k/3 = 1/3 implies k = 1

The correct answer is D.

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Wed Sep 28, 2011 5:55 pm

if two points are on the same line, they belong to the function of that line and may be derived by the function of that same line

we are given the slope from the function 3y=x+7, it's 1/3 as y=x/3+7/3

now from the slope formula we set the proportion (b+k-b)/(a+3-a)=1/3 or k/3=1/3 where k=1

factor26 wrote:In the xy-coordinate system, if (a, b) and (a + 3, b + k) are two points on the line defined by the equation x = 3y - 7, then k =
(A) 9
(B) 3
(C) 7/3
(D) 1
(E) 1/3

OA IS D ... can someone please give me a step by step on how to solve this and insight on topic being tested?

Thanks!

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